Math 115 Name: Key
Quiz 3 September
20, 2013
1. Andy and Terry split a cake by the dividerchooser method. Andy, the divider, likes chocolate icing twice as much as vanilla. Show 2 different ways that Andy might split the cake to ensure he gets a “fair” piece.
1 option is to make each share contain Swap
1 choc for 2 white and it is still fair (to Andy)
2 choc, 2 white: {7,8,1,2} / {3,4,5,6} for example, {5,6,7,8,1} / {2, 3, 4} is fair
2. Three players, Ali, Bo, and Caz, divide the 13 items shown by the method of markers.
1 2 3 4 5 6 7 8 9 10
11 12
13
Which items: go to Ali? 913
go to Bo? 1  3
go to Caz? 6 7
are (initially) left over? 4, 5, 8
2b. According to the rules of this method, how should the leftovers be allocated? EXPLAIN your answer in a complete English sentence.
Since everyone has
received a fair share already, no matter what allocation of the leftovers is
chose it will still be fair – so it doesn’t matter.

Games 
Toys 
Clothes 
Alex 
30 
18 
12 
Brenda 
36 
16 
20 
3. 2 sisters, Alex and Brenda, divide some games, some clothes, and some toys by the method of sealed bids.
The bids (in $) are as follows:
a. Find the value of each sister’s fair share
Alex,
60/2= $30
Brenda, 72/2 = $36
b. Determine what items each sister gets. Then compute the payments in the first settlement, and finally determine the result after the final settlement.
Alex
gets the toys (value of $18 to her), Brenda gets the
games and clothes ($56 to her)
Brenda
then pays $20, while Alex takes $12.
There is then an $8 surplus, so each gets $4 from that. End result:
Alex gets the toys and $16, Brenda gets the game and clothes, and pays
$16.